In this article, the effects of different diverging-converging pore geometries were investigated, and the microscale fluid flow and effective hydraulic properties from these pores were compared with that of a pipe from viscous to inertial laminar flow regimes. The flow fields are obtained using computational fluid dynamics, and the comparative analysis is based on a new dimensionless hydraulic shape factor β, which is the "specific surface" scaled by the length of pores. Results from all diverging-converging pores show an inverse pattern in velocity and vorticity distributions relative to the pipe flow. The hydraulic conductivity K of all pores is dependent on and can be predicted from β with a power function with an exponent of 3/2. The differences in K are due to the differences in distribution of local friction drag on the pore walls. At Reynolds number (Re) ∼ 0 flows, viscous eddies are found to exist almost in all pores in different sizes, but not in the pipe. Eddies grow when Re →1 and leads to the failure of Darcy's law. During non-Darcy or Forchheimer flows, the apparent hydraulic conductivity Ka decreases due to the growth of eddies, which constricts the bulk flow region. At Re > 1, the rate of decrease in Ka increases, and at Re >> 1, it decreases to where the change in Ka ≈ 0, and flows once again exhibits a Darcy-type relationship. The degree of nonlinearity during non-Darcy flow decreases for pores with increasing β. The nonlinear flow behavior becomes weaker as β increases to its maximum value in the pipe, which shows no nonlinearity in the flow; in essence, Darcy's law stays valid in the pipe at all laminar flow conditions. The diverging-converging geometry in pores plays a critical role in modifying the intrapore fluid flow, implying that this property should be incorporated in effective larger-scale models, e.g., pore-network models.


Civil, Architectural and Environmental Engineering


This work is supported as part of the Center for Frontiers of Subsurface Energy Security (CFSES) at the University of Texas at Austin, an Energy Frontier Research Center funded by the U.S.Department of Energy, Office of Science, Office of Basic Energy Sciences under award DE-SC0001114. Additional support was provided by theGeology Foundation of the University of Texas.

Keywords and Phrases

Comparative analysis; Degree of non-linearity; Hydraulic parameters; Hydraulic properties; Laminar flow conditions; Laminar flow regimes; Pore-network models; Vorticity distribution; Computational fluid dynamics; Flow fields; Groundwater flow; Hydraulic conductivity; Laminar flow; Reynolds number; Seepage; Geometry; Darcy law; Fluid flow; Nonlinearity; Pore space

International Standard Serial Number (ISSN)

0043-1397; 1944-7973

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2013 American Geophysical Union (AGU), All rights reserved.

Publication Date

01 Feb 2013